Finite Group Databasebeta

← #10596124⋊C3 #13153044

Subgroups — #10596124⋊C3 #13153044

Order 1728.

1289 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
2C22×C4⋊((C3⋊D3)⋊C3)C211yesmaximal, characteristic, complemented
3H(3,𝔽3)×#123C211yesmaximal, characteristic, complemented
4#64146⋊C3C211yesmaximal, characteristic, complemented
5#64138⋊C3C211yesmaximal, characteristic, complemented
6#64104⋊C3C212yesmaximal, complemented
7#64103⋊C3C212yesmaximal, complemented
8#64093⋊C3C212yesmaximal, complemented
9#64091⋊C3C212yesmaximal, complemented
10#64091⋊C3C211yesmaximal, characteristic, complemented
11C22⋊C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
12#10596124C311yesmaximal, characteristic, complemented
13C3×#5653—31nomaximal
14C23×(C3⋊D3)⋊C3C2211yescharacteristic
15C23×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
16C23×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
17C2×D4×H(3,𝔽3)C2211yescharacteristic
18C22×C4×H(3,𝔽3)C2211yescharacteristic, complemented
19C2×#638⋊C3C2211yescharacteristic
20C2×#638⋊C3C2211yescharacteristic, complemented
21C2×#638⋊C3C2212yescomplemented
22D4×(C3⋊D3)⋊C3—24no—
23C2×C4⋊((C3⋊D3)⋊C3)—24no—
24C2×C4⋊((C3⋊D3)⋊C3)C2212yes—
25C2×C4⋊((C3⋊D3)⋊C3)C2212yescomplemented
26C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic, complemented
27C2×C4⋊((C3⋊D3)⋊C3)C2212yescomplemented
28C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
29C2×C4×(C3⋊D3)⋊C3C2212yescomplemented
30C4⋊C4×H(3,𝔽3)C2212yescomplemented
31C22⋊C4×H(3,𝔽3)C2211yescharacteristic, complemented
32C22⋊C4×H(3,𝔽3)C2212yescomplemented
33#3757⋊C3C2211yescharacteristic, complemented
34#3752⋊C3C2212yescomplemented
35#3752⋊C3C2212yescomplemented
36#3752⋊C3C2212yescomplemented
37#3752⋊C3C2212yescomplemented
38#3750⋊C3C2212yescomplemented
39C2×D4×C3⋊D3C2×C311yescharacteristic, complemented
40C22×C4⋊(C3⋊D3)C2×C311yescharacteristic, complemented
41C2×C3×D3×D4—31no—
42C22×C3×D12—31no—
43C32×#123—21no—
44C32×#123D311yescharacteristic, complemented
45C32×#123C2×C311yescharacteristic, complemented
46#64146C2×C311yescharacteristic, complemented
47#64138C2×C311yescharacteristic, complemented
48#64104C2×C312yescomplemented
49#64103C2×C312yescomplemented
50#64093C2×C312yescomplemented
51#64091C2×C312yescomplemented
52#64091C2×C311yescharacteristic, complemented
53C22⋊C4×C3⋊D3C2×C311yescharacteristic, complemented
54C3×#937—31no—
55C3×#929—31no—
56C3×#895—32no—
57C3×#894—32no—
58C3×#884—32no—
59C3×#882—32no—
60C3×#882—31no—
61C3×D3×C22⋊C4—31no—
62C23×H(3,𝔽3)C2311yescharacteristic
63C23×H(3,𝔽3)C2311yescharacteristic
64C22×(C3⋊D3)⋊C3—22no—
65C22×(C3⋊D3)⋊C3—22no—
66C22×(C3⋊D3)⋊C3—42no—
67C22×(C3⋊D3)⋊C3—42no—
68C22×(C3⋊D3)⋊C3—42no—
69C22×(C3⋊D3)⋊C3D414yescomplemented
70C22×(C3⋊D3)⋊C3C2312yes—
71C22×(C3⋊D3)⋊C3C2311yescharacteristic
72C22×(C3⋊D3)⋊C3C2311yescharacteristic
73C22×(C3⋊D3)⋊C3C2311yescharacteristic
74D4×H(3,𝔽3)—22no—
75C2×C4×H(3,𝔽3)—22no—
76C2×C4×H(3,𝔽3)C2311yescharacteristic
77C2×C4×H(3,𝔽3)C2312yes—
78C2×C4×H(3,𝔽3)C2312yes—
79#638⋊C3—22no—
80#638⋊C3—22no—
81#638⋊C3—42no—
82C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
83C2×(C3⋊Dic3)⋊C3C2312yes—
84C4⋊((C3⋊D3)⋊C3)—24no—
85C4⋊((C3⋊D3)⋊C3)—24no—
86C4⋊((C3⋊D3)⋊C3)—22no—
87C4⋊((C3⋊D3)⋊C3)—42no—
88C4×(C3⋊D3)⋊C3—22no—
89C4×(C3⋊D3)⋊C3—42no—
90C3×#534—91no—
91#5653—31no—
92#5653—91no—
93C23×C3⋊D3C22×C311yescharacteristic
94C23×C3⋊D3C22×C311yescharacteristic, complemented
95C23×C3⋊D3C22×C311yescharacteristic, complemented
96C23×C3×D3—31no—
97C23×C3×D3—31no—
98C23×C3×D3—31no—
99C2×C32×D4—21no—
100C2×C32×D4C2×D311yescharacteristic
101C2×C32×D4C22×C311yescharacteristic
102C22×C32×C4—21no—
103C22×C32×C4C2×D311yescharacteristic, complemented
104C22×C32×C4C22×C311yescharacteristic, complemented
105C2×#638C22×C311yescharacteristic
106C2×#638C22×C311yescharacteristic, complemented
107C2×#638C22×C312yescomplemented
108D4×C3⋊D3—24no—
109C2×C4⋊(C3⋊D3)—24no—
110C2×C4⋊(C3⋊D3)C22×C312yes—
111C2×C4⋊(C3⋊D3)C22×C312yescomplemented
112C2×C4⋊(C3⋊D3)C22×C311yescharacteristic, complemented
113C2×C4⋊(C3⋊D3)C22×C312yescomplemented
114C2×C4×C3⋊D3C22×C311yescharacteristic, complemented
115C2×C4×C3⋊D3C22×C312yescomplemented
116C2×C3×#67—31no—
117C2×C3×#67—31no—
118C2×C3×#67—32no—
119C3×D3×D4—64no—
120C2×C3×D12—32no—
121C2×C3×D12—32no—
122C2×C3×D12—31no—
123C2×C3×D12—32no—
124C2×C3×D12—64no—
125C2×C3×C4×D3—31no—
126C2×C3×C4×D3—32no—
127C32×C4⋊C4—22no—
128C32×C4⋊C4C2×D312yescomplemented
129C32×C4⋊C4C22×C312yescomplemented
130C32×C22⋊C4—21no—
131C32×C22⋊C4—22no—
132C32×C22⋊C4C2×D311yescharacteristic, complemented
133C32×C22⋊C4C2×D312yescomplemented
134C32×C22⋊C4C22×C311yescharacteristic, complemented
135C32×C22⋊C4C22×C312yescomplemented
136#3757C22×C311yescharacteristic, complemented
137#3752C22×C312yescomplemented
138#3752C22×C312yescomplemented
139#3752C22×C312yescomplemented
140#3752C22×C312yescomplemented
141#3750C22×C312yescomplemented
142C3×#217—31no—
143C3×(C2×D3)⋊C4—32no—
144C3×(C2×D3)⋊C4—32no—
145C3×(C2×D3)⋊C4—32no—
146C3×(C2×D3)⋊C4—32no—
147C3×Dic3⋊C4—32no—
148C22×H(3,𝔽3)—22no—
149C22×H(3,𝔽3)—21no—
150C22×H(3,𝔽3)—22no—
151C22×H(3,𝔽3)C2×D412yes—
152C22×H(3,𝔽3)C2411yescharacteristic
153C2×(C3⋊D3)⋊C3—22no—
154C2×(C3⋊D3)⋊C3—22no—
155C2×(C3⋊D3)⋊C3—22no—
156C2×(C3⋊D3)⋊C3—21no—
157C2×(C3⋊D3)⋊C3—22no—
158C2×(C3⋊D3)⋊C3—22no—
159C2×(C3⋊D3)⋊C3—22no—
160C2×(C3⋊D3)⋊C3—44no—
161C2×(C3⋊D3)⋊C3—44no—
162C2×(C3⋊D3)⋊C3—44no—
163C2×(C3⋊D3)⋊C3C2×D412yes—
164C2×(C3⋊D3)⋊C3C2×D412yes—
165C4×H(3,𝔽3)—21no—
166C4×H(3,𝔽3)—22no—
167C4×H(3,𝔽3)—22no—
168(C3⋊Dic3)⋊C3—21no—
169(C3⋊Dic3)⋊C3—22no—
170C22×C3×D4—91no—
171C22×C3×D4—91no—
172C2×D3×D4—31no—
173C2×D3×D4—91no—
174C22×D12—31no—
175C22×D12—91no—
176C3×#123—31no—
177C3×#123—31no—
178C3×#123—61no—
179C3×#123—92no—
180C3×#123—91no—
181C3×#123C3×D311yescharacteristic
182C3×#121—92no—
183C3×#121—92no—
184C3×#120—91no—
185C3×#120—92no—
186C3×#120—91no—
187C2×C3×C22⋊C4—91no—
188#937—31no—
189#937—91no—
190#929—31no—
191#929—91no—
192#895—32no—
193#895—92no—
194#894—32no—
195#894—92no—
196#884—32no—
197#884—92no—
198#882—32no—
199#882—31no—
200#882—92no—
201#882—91no—
202D3×C22⋊C4—31no—
203D3×C22⋊C4—91no—
204C23×C32—21no—
205C23×C32—21no—
206C23×C32C22×D311yescharacteristic
207C23×C32C22×D311yescharacteristic
208C23×C32C23×C311yescharacteristic
209C23×C32C23×C311yescharacteristic
210C22×C3⋊D3—22no—
211C22×C3⋊D3—22no—
212C22×C3⋊D3—42no—
213C22×C3⋊D3—42no—
214C22×C3⋊D3—42no—
215C22×C3⋊D3C3×D414yescomplemented
216C22×C3⋊D3C23×C312yes—
217C22×C3⋊D3C23×C311yescharacteristic
218C22×C3⋊D3C23×C311yescharacteristic
219C22×C3⋊D3C23×C311yescharacteristic
220C22×C3×D3—31no—
221C22×C3×D3—31no—
222C22×C3×D3—34no—
223C22×C3×D3—32no—
224C22×C3×D3—31no—
225C22×C3×D3—62no—
226C22×C3×D3—62no—
227C22×C3×D3—122no—
228C22×C3×D3—122no—
229C22×C3×D3—122no—
230C32×D4—22no—
231C32×D4—22no—
232C32×D4—42no—
233C2×C32×C4—22no—
234C2×C32×C4—22no—
235C2×C32×C4—22no—
236C2×C32×C4—22no—
237C2×C32×C4—21no—
238C2×C32×C4—42no—
239C2×C32×C4C22×D312yes—
240C2×C32×C4C22×D312yes—
241C2×C32×C4C22×D311yescharacteristic
242C2×C32×C4C23×C312yes—
243C2×C32×C4C23×C312yes—
244C2×C32×C4C23×C311yescharacteristic
245#638—22no—
246#638—22no—
247#638—42no—
248C2×C3⋊Dic3C23×C311yescharacteristic
249C2×C3⋊Dic3C23×C312yes—
250C4⋊(C3⋊D3)—24no—
251C4⋊(C3⋊D3)—24no—
252C4⋊(C3⋊D3)—22no—
253C4⋊(C3⋊D3)—42no—
254C4×C3⋊D3—22no—
255C4×C3⋊D3—42no—
256C3×#67—62no—
257C3×#67—62no—
258C3×#67—122no—
259C2×C3×Dic3—31no—
260C2×C3×Dic3—32no—
261C3×D12—64no—
262C3×D12—64no—
263C3×D12—62no—
264C3×D12—122no—
265C3×C4×D3—62no—
266C3×C4×D3—122no—
267#534—91noSylow
268C2×H(3,𝔽3)—22no—
269C2×H(3,𝔽3)—41no—
270C2×H(3,𝔽3)C22×D411yescharacteristic
271C2×H(3,𝔽3)H(5,𝔽2)12yes—
272(C3⋊D3)⋊C3—22no—
273(C3⋊D3)⋊C3—22no—
274(C3⋊D3)⋊C3—42no—
275(C3⋊D3)⋊C3—41no—
276C24×C3—91no—
277C24×C3—91no—
278C24×C3—91no—
279C23×D3—31no—
280C23×D3—31no—
281C23×D3—31no—
282C23×D3—91no—
283C23×D3—91no—
284C23×D3—91no—
285C2×C3×D4—31no—
286C2×C3×D4—31no—
287C2×C3×D4—61no—
288C2×C3×D4—92no—
289C2×C3×D4—92no—
290C2×C3×D4—91no—
291C2×C3×D4—92no—
292C2×C3×D4—91no—
293C2×C3×D4—91no—
294C2×C3×D4—92no—
295C2×C3×D4—184no—
296C2×C3×D4—184no—
297C2×C3×D4C2×C3×D311yescharacteristic
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—61no—
301C22×C3×C4—91no—
302C22×C3×C4—92no—
303C22×C3×C4C2×C3×D311yescharacteristic
304C2×#67—31no—
305C2×#67—31no—
306C2×#67—32no—
307C2×#67—91no—
308C2×#67—91no—
309C2×#67—92no—
310D3×D4—64no—
311D3×D4—184no—
312C2×D12—32no—
313C2×D12—32no—
314C2×D12—31no—
315C2×D12—32no—
316C2×D12—64no—
317C2×D12—92no—
318C2×D12—92no—
319C2×D12—91no—
320C2×D12—92no—
321C2×D12—184no—
322C2×C4×D3—31no—
323C2×C4×D3—32no—
324C2×C4×D3—91no—
325C2×C4×D3—92no—
326C3×C4⋊C4—32no—
327C3×C4⋊C4—32no—
328C3×C4⋊C4—62no—
329C3×C4⋊C4—92no—
330C3×C4⋊C4C2×C3×D312yes—
331C3×C22⋊C4—31no—
332C3×C22⋊C4—32no—
333C3×C22⋊C4—31no—
334C3×C22⋊C4—32no—
335C3×C22⋊C4—61no—
336C3×C22⋊C4—62no—
337C3×C22⋊C4—92no—
338C3×C22⋊C4—92no—
339C3×C22⋊C4—92no—
340C3×C22⋊C4—92no—
341C3×C22⋊C4—91no—
342C3×C22⋊C4C2×C3×D311yescharacteristic
343C3×C22⋊C4C2×C3×D312yes—
344#217—31no—
345#217—91no—
346(C2×D3)⋊C4—32no—
347(C2×D3)⋊C4—32no—
348(C2×D3)⋊C4—32no—
349(C2×D3)⋊C4—32no—
350(C2×D3)⋊C4—92no—
351(C2×D3)⋊C4—92no—
352(C2×D3)⋊C4—92no—
353(C2×D3)⋊C4—92no—
354Dic3⋊C4—32no—
355Dic3⋊C4—92no—
356C22×C32—22no—
357C22×C32—22no—
358C22×C32—21no—
359C22×C32—22no—
360C22×C32—21no—
361C22×C32—22no—
362C22×C32—21no—
363C22×C32—22no—
364C22×C32—42no—
365C22×C32—41no—
366C22×C32—42no—
367C22×C32D3×D412yes—
368C22×C32C2×C3×D412yes—
369C22×C32C23×D311yescharacteristic
370C22×C32C24×C311yescharacteristic
371C2×C3⋊D3—22no—
372C2×C3⋊D3—22no—
373C2×C3⋊D3—22no—
374C2×C3⋊D3—21no—
375C2×C3⋊D3—22no—
376C2×C3⋊D3—22no—
377C2×C3⋊D3—22no—
378C2×C3⋊D3—44no—
379C2×C3⋊D3—44no—
380C2×C3⋊D3—44no—
381C2×C3⋊D3C2×C3×D412yes—
382C2×C3⋊D3C2×C3×D412yes—
383C2×C3×D3—32no—
384C2×C3×D3—32no—
385C2×C3×D3—62no—
386C2×C3×D3—62no—
387C2×C3×D3—62no—
388C2×C3×D3—61no—
389C2×C3×D3—62no—
390C2×C3×D3—62no—
391C2×C3×D3—62no—
392C2×C3×D3—124no—
393C2×C3×D3—124no—
394C2×C3×D3—124no—
395C32×C4—21no—
396C32×C4—22no—
397C32×C4—22no—
398C32×C4—21no—
399C32×C4—22no—
400C32×C4—22no—
401C32×C4—42no—
402C32×C4—42no—
403C32×C4—41no—
404C3⋊Dic3—21no—
405C3⋊Dic3—22no—
406C3×Dic3—61no—
407C3×Dic3—62no—
408C22×D4—91no—
409C22×D4—91no—
410#123—91no—
411#123—92no—
412#123(C3⋊D3)⋊C311yescharacteristic, complemented
413#121—92no—
414#121—92no—
415#120—91no—
416#120—92no—
417#120—91no—
418C2×C22⋊C4—91no—
419H(3,𝔽3)#53411yescharacteristic, complemented, Sylow
420C23×C3—31no—
421C23×C3—31no—
422C23×C3—31no—
423C23×C3—31no—
424C23×C3—61no—
425C23×C3—61no—
426C23×C3—91no—
427C23×C3—91no—
428C23×C3—94no—
429C23×C3—92no—
430C23×C3—91no—
431C23×C3—182no—
432C23×C3—182no—
433C23×C3—362no—
434C23×C3—362no—
435C23×C3—362no—
436C23×C3C22×C3×D311yescharacteristic
437C23×C3C22×C3×D311yescharacteristic
438C22×D3—31no—
439C22×D3—31no—
440C22×D3—34no—
441C22×D3—32no—
442C22×D3—31no—
443C22×D3—62no—
444C22×D3—62no—
445C22×D3—91no—
446C22×D3—91no—
447C22×D3—94no—
448C22×D3—92no—
449C22×D3—91no—
450C22×D3—122no—
451C22×D3—122no—
452C22×D3—122no—
453C22×D3—182no—
454C22×D3—182no—
455C22×D3—362no—
456C22×D3—362no—
457C22×D3—362no—
458C3×D4—22no—
459C3×D4—62no—
460C3×D4—62no—
461C3×D4—122no—
462C3×D4—184no—
463C3×D4—184no—
464C3×D4—182no—
465C3×D4—182no—
466C3×D4—182no—
467C3×D4—362no—
468C3×D4—362no—
469C2×C3×C4—22no—
470C2×C3×C4—32no—
471C2×C3×C4—32no—
472C2×C3×C4—31no—
473C2×C3×C4—32no—
474C2×C3×C4—32no—
475C2×C3×C4—31no—
476C2×C3×C4—62no—
477C2×C3×C4—62no—
478C2×C3×C4—62no—
479C2×C3×C4—62no—
480C2×C3×C4—61no—
481C2×C3×C4—92no—
482C2×C3×C4—91no—
483C2×C3×C4—122no—
484C2×C3×C4—182no—
485C2×C3×C4—362no—
486C2×C3×C4C22×C3×D312yes—
487C2×C3×C4C22×C3×D312yes—
488C2×C3×C4C22×C3×D311yescharacteristic
489#67—62no—
490#67—62no—
491#67—122no—
492#67—182no—
493#67—182no—
494#67—362no—
495C2×Dic3—31no—
496C2×Dic3—32no—
497C2×Dic3—91no—
498C2×Dic3—92no—
499D12—64no—
500D12—64no—
501D12—62no—
502D12—122no—
503D12—184no—
504D12—184no—
505D12—182no—
506D12—362no—
507C4×D3—62no—
508C4×D3—122no—
509C4×D3—182no—
510C4×D3—362no—
511C2×C32—22no—
512C2×C32—22no—
513C2×C32—21no—
514C2×C32—22no—
515C2×C32—42no—
516C2×C32—41no—
517C2×C32—41no—
518C2×C32—81no—
519C2×C32C2×D3×D411yescharacteristic
520C2×C32#100912yes—
521C2×C32C22×C3×D411yescharacteristic
522C2×C32C3×H(5,𝔽2)12yes—
523C3⋊D3—22no—
524C3⋊D3—22no—
525C3⋊D3—42no—
526C3⋊D3—41no—
527C3×D3—62no—
528C3×D3—62no—
529C3×D3—122no—
530C3×D3—121no—
531C24—91no—
532C24—91no—
533C24—91no—
534C2×D4—91no—
535C2×D4—91no—
536C2×D4—92no—
537C2×D4—92no—
538C2×D4—91no—
539C2×D4—92no—
540C2×D4—92no—
541C2×D4—184no—
542C2×D4—184no—
543C2×D4C2×(C3⋊D3)⋊C311yescharacteristic
544C22×C4—91no—
545C22×C4—92no—
546C22×C4C2×(C3⋊D3)⋊C311yescharacteristic, complemented
547C4⋊C4—92no—
548C4⋊C4C2×(C3⋊D3)⋊C312yescomplemented
549C22⋊C4—91no—
550C22⋊C4—92no—
551C22⋊C4—92no—
552C22⋊C4—92no—
553C22⋊C4—92no—
554C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic, complemented
555C22⋊C4C2×(C3⋊D3)⋊C312yescomplemented
556C22×C3—22no—
557C22×C3—21no—
558C22×C3—22no—
559C22×C3—31no—
560C22×C3—31no—
561C22×C3—32no—
562C22×C3—32no—
563C22×C3—62no—
564C22×C3—62no—
565C22×C3—61no—
566C22×C3—62no—
567C22×C3—61no—
568C22×C3—62no—
569C22×C3—61no—
570C22×C3—62no—
571C22×C3—92no—
572C22×C3—92no—
573C22×C3—122no—
574C22×C3—121no—
575C22×C3—122no—
576C22×C3—182no—
577C22×C3—182no—
578C22×C3—182no—
579C22×C3—181no—
580C22×C3—182no—
581C22×C3—182no—
582C22×C3—182no—
583C22×C3—364no—
584C22×C3—364no—
585C22×C3—364no—
586C22×C3C3×D3×D412yes—
587C22×C3C23×C3×D311yescharacteristic
588C2×D3—32no—
589C2×D3—32no—
590C2×D3—62no—
591C2×D3—62no—
592C2×D3—62no—
593C2×D3—61no—
594C2×D3—62no—
595C2×D3—62no—
596C2×D3—62no—
597C2×D3—92no—
598C2×D3—92no—
599C2×D3—124no—
600C2×D3—124no—
601C2×D3—124no—
602C2×D3—182no—
603C2×D3—182no—
604C2×D3—182no—
605C2×D3—181no—
606C2×D3—182no—
607C2×D3—182no—
608C2×D3—182no—
609C2×D3—364no—
610C2×D3—364no—
611C2×D3—364no—
612C3×C4—21no—
613C3×C4—22no—
614C3×C4—22no—
615C3×C4—61no—
616C3×C4—62no—
617C3×C4—62no—
618C3×C4—62no—
619C3×C4—61no—
620C3×C4—62no—
621C3×C4—122no—
622C3×C4—121no—
623C3×C4—122no—
624C3×C4—181no—
625C3×C4—182no—
626Dic3—61no—
627Dic3—62no—
628Dic3—181no—
629Dic3—182no—
630C32—21no—
631C32#565311yescharacteristic, complemented
632C32C3×#53411yescharacteristic, complemented
633C23—91no—
634C23—91no—
635C23—94no—
636C23—91no—
637C23—92no—
638C23—182no—
639C23—182no—
640C23—362no—
641C23—362no—
642C23—362no—
643C23C22×(C3⋊D3)⋊C311yescharacteristic
644C23C22×(C3⋊D3)⋊C311yescharacteristic
645D4—22no—
646D4—184no—
647D4—184no—
648D4—182no—
649D4—182no—
650D4—182no—
651D4—362no—
652D4—362no—
653C2×C4—22no—
654C2×C4—92no—
655C2×C4—91no—
656C2×C4—182no—
657C2×C4—362no—
658C2×C4C22×(C3⋊D3)⋊C312yes—
659C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
660C2×C4C22×(C3⋊D3)⋊C312yes—
661C2×C3—22no—
662C2×C3—31no—
663C2×C3—31no—
664C2×C3—32no—
665C2×C3—32no—
666C2×C3—41no—
667C2×C3—62no—
668C2×C3—62no—
669C2×C3—61no—
670C2×C3—62no—
671C2×C3—122no—
672C2×C3—121no—
673C2×C3—121no—
674C2×C3—182no—
675C2×C3—182no—
676C2×C3—241no—
677C2×C3—362no—
678C2×C3—361no—
679C2×C3C2×C3×D3×D411yescharacteristic
680C2×C3C3×#100912yes—
681D3—62no—
682D3—62no—
683D3—122no—
684D3—121no—
685D3—182no—
686D3—182no—
687D3—362no—
688D3—361no—
689C22—22no—
690C22—21no—
691C22—22no—
692C22—92no—
693C22—92no—
694C22—182no—
695C22—182no—
696C22—182no—
697C22—181no—
698C22—182no—
699C22—182no—
700C22—182no—
701C22—364no—
702C22—364no—
703C22—364no—
704C22D4×(C3⋊D3)⋊C312yes—
705C22C23×(C3⋊D3)⋊C311yescharacteristic
706C4—22no—
707C4—21no—
708C4—22no—
709C4—181no—
710C4—182no—
711C3—31no—
712C3—31no—
713C3—61no—
714C3C3×#565311yescharacteristic
715C2—22no—
716C2—41no—
717C2—182no—
718C2—182no—
719C2—362no—
720C2—361no—
721C2C2×D4×(C3⋊D3)⋊C311yescharacteristic
722C2#1172263812yes—
subgroupG/H
centerC22C23×(C3⋊D3)⋊C3
commutator, cosocleC22×C32C24×C3
Frattini, socleC22×C3C23×C3×D3
FittingH(3,𝔽3)×#123C2
hypercenter#123(C3⋊D3)⋊C3
hypocenterC32C3×#534
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #123

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×D4×(C3⋊D3)⋊C3C2semidirect
2. C22×C4⋊((C3⋊D3)⋊C3)C2semidirect
3. H(3,𝔽3)×#123C2semidirect
4. #64146⋊C3C2semidirect
5. #64138⋊C3C2semidirect
6. #64104⋊C3C2semidirect
7. #64103⋊C3C2semidirect
8. #64093⋊C3C2semidirect
9. #64091⋊C3C2semidirect
10. #64091⋊C3C2semidirect
11. C22⋊C4×(C3⋊D3)⋊C3C2semidirect
12. #10596124C3semidirect
15. C23×(C3⋊D3)⋊C3C22semidirect
16. C23×(C3⋊D3)⋊C3C22semidirect
18. C22×C4×H(3,𝔽3)C22semidirect
20. C2×#638⋊C3C22semidirect
21. C2×#638⋊C3C22semidirect
25. C2×C4⋊((C3⋊D3)⋊C3)C22semidirect
26. C2×C4⋊((C3⋊D3)⋊C3)C22semidirect
27. C2×C4⋊((C3⋊D3)⋊C3)C22semidirect
28. C2×C4×(C3⋊D3)⋊C3C22semidirect
29. C2×C4×(C3⋊D3)⋊C3C22semidirect
30. C4⋊C4×H(3,𝔽3)C22semidirect
31. C22⋊C4×H(3,𝔽3)C22semidirect
32. C22⋊C4×H(3,𝔽3)C22semidirect
33. #3757⋊C3C22semidirect
34. #3752⋊C3C22semidirect
35. #3752⋊C3C22semidirect
36. #3752⋊C3C22semidirect
37. #3752⋊C3C22semidirect
38. #3750⋊C3C22semidirect
39. C2×D4×C3⋊D3C2×C3semidirect
40. C22×C4⋊(C3⋊D3)C2×C3semidirect
44. C32×#123D3semidirect
45. C32×#123C2×C3semidirect
46. #64146C2×C3semidirect
47. #64138C2×C3semidirect
48. #64104C2×C3semidirect
49. #64103C2×C3semidirect
50. #64093C2×C3semidirect
51. #64091C2×C3semidirect
52. #64091C2×C3semidirect
53. C22⋊C4×C3⋊D3C2×C3semidirect
69. C22×(C3⋊D3)⋊C3D4semidirect
94. C23×C3⋊D3C22×C3semidirect
95. C23×C3⋊D3C22×C3semidirect
103. C22×C32×C4C2×D3semidirect
104. C22×C32×C4C22×C3semidirect
106. C2×#638C22×C3semidirect
107. C2×#638C22×C3semidirect
111. C2×C4⋊(C3⋊D3)C22×C3semidirect
112. C2×C4⋊(C3⋊D3)C22×C3semidirect
113. C2×C4⋊(C3⋊D3)C22×C3semidirect
114. C2×C4×C3⋊D3C22×C3semidirect
115. C2×C4×C3⋊D3C22×C3semidirect
128. C32×C4⋊C4C2×D3semidirect
129. C32×C4⋊C4C22×C3semidirect
132. C32×C22⋊C4C2×D3semidirect
133. C32×C22⋊C4C2×D3semidirect
134. C32×C22⋊C4C22×C3semidirect
135. C32×C22⋊C4C22×C3semidirect
136. #3757C22×C3semidirect
137. #3752C22×C3semidirect
138. #3752C22×C3semidirect
139. #3752C22×C3semidirect
140. #3752C22×C3semidirect
141. #3750C22×C3semidirect
215. C22×C3⋊D3C3×D4semidirect
412. #123(C3⋊D3)⋊C3semidirect
419. H(3,𝔽3)#534semidirect
546. C22×C4C2×(C3⋊D3)⋊C3semidirect
548. C4⋊C4C2×(C3⋊D3)⋊C3semidirect
554. C22⋊C4C2×(C3⋊D3)⋊C3semidirect
555. C22⋊C4C2×(C3⋊D3)⋊C3semidirect
631. C32#5653semidirect
632. C32C3×#534semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×D4×(C3⋊D3)⋊C32
C22×C4⋊((C3⋊D3)⋊C3)2
H(3,𝔽3)×#1232
#64146⋊C32
#64138⋊C32
#64104⋊C32
#64103⋊C32
#64093⋊C32
#64091⋊C32
C22⋊C4×(C3⋊D3)⋊C32
#105961243
C3×#56533